Keane said: "If people want to criticise me that's okay - but I try not to take much notice. I ask the same question to myself every morning: Have I got something to offer Manchester United? At this moment, the answer is always yes.
"Without a doubt, I feel I can compete with players like Gerrard and Vieira. When I feel I can't do that, then I'll know.
"The manager was very complimentary about Gerrard and there's no doubt he is a very good player - but I still feel I am better than him and that's not being big-headed.
"You look at Gerrard last season and he didn't kick a ball for the first three-and-a-half months.
The 33-year-old star, turning his delusional eye to the Arsenal captain Patrick Vieira, added: "You look at Vieira. I always ask questions of people in certain big games and I just look at when Arsenal played against Chelsea in the Champions League. In the second half of that match at Highbury, a lot of their players weren't there to be seen - so you can pick on any players at different parts of the season.
"I still look at the so-called other top players in England and again, I look at myself every day of the week and ask questions. But put me up against any of those players and I will win some battles and lose some.
"That's football - but I still fancy my chances against anyone."